Aircraft: B737
Phase of flight: Initial Approach
Anomaly: ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance

On the WARRR 1 STAR to ATL; we were at 12;000 ft; following the RNAV STAR. There was much congestion on the ATL Approach frequency; and we were assigned the Runway 28 transition; which requires a downwind turn; during which are several step-down fixes. Another aircraft; (other carrier) was on the frequency; and both of us (Company) and (other carrier) asked ATC to verify the call signs multiple times. At no time did I hear ATC warn 'Similar-sounding call signs; use caution.' While still on the 45-degree angle to the RNAV downwind; I heard 'our call sign; descend and maintain 3000 ft.' I read back our call sign leaving 12;000 ft feet for 3000 ft.' As we were passing 6000 ft; ATC queried us; 'where are you going?' I replied; 'we are descending to 3000 ft as directed.' ATC told us to stop descent at I believe; 5000 ft; which we did. The FO and I discussed the presence of (other carrier) on the same arrival. The Controller seemed to have a very heavy workload this morning; as ATL was using three westbound runways for approach and two runways for departures. ATC told us that 'we should know that he doesn't usually descend aircraft to 3000 feet so far from the airport.' I replied that we only complied with our ATC instruction; and had indeed read back the ATC clearance. After that event; we modified our call sign to 'Company XXX; Company'; to avoid further confusion with the similar-sounding 'other carrier XXXX'.In cases where ATC seems to be getting overwhelmed; we can help out by clarifying our call signs; and verifying the instructions by ATC. ATC did not respond to my readback of the descent to 3000; nor did ATC make any mention of my leaving 12;000 on the arrival. For our part; I believe that modifying the call signs to 'Company XXXX; Company' may have helped the Controller avoid conflict. We were on arrival into Atlanta; I was the Pilot Flying; radio frequencies were very busy; Captain checked-on with Approach; gave ATC current ATIS info and we were descending via the arrival. I'm used to Atlanta bringing us fairly high (around 10;000 ft) on downwind before they expect an expeditionary descent to about 4;000 ft for a base turn and I usually call for flaps 5 to expedite descent for the base turn into Atlanta. I don't fly into this airport very often and if memory serves me correctly; I always seem to land on the north side; with one landing that I can recall on 27L from a north approach; and this was my first approach from the south and we were advised to plan on a visual to 28. We were given a clearance to descend; I cannot recall the altitude; but I believe it was between 6000 ft and 4000 ft. I dialed in the altitude; we both (Captain and I) pointed to the Altitude window and confirmed the altitude; and I began a descent using Level Change but at flaps 0 simply because we were so far. I got the impression the Captain was expecting a descent a little more expeditiously. That was just my impression. I also recall we were at 210 knots so we were barely descending at around 1000 fpm. As we descended from our previously assigned altitude that was 12;000 ft and were about to descend through 10;000 ft; Atlanta Approach called us and said (call sign) stop your descent! Maintain 10;000 ft. So we looked at each other startled; complied and maintained 10;000 ft. Soon after we heard another carrier flight with a similar call sign and we realized there was confusion on the call sign. As we continued at 10;000 ft; the same Controller called us back and advised us that in the future Atlanta Approach would never clear an aircraft to such a low altitude that far out from the airport. I didn't think the altitude was excessively low under normal circumstances; but I wasn't too familiar with Atlanta Approach from the southwest of the airport. We continued complying with ATC instructions and we both noticed the same Controller getting frustrated and miscommunicating with other aircraft including another Company aircraft and another carrier. Before we switched over to Tower for a visual to Runway 28; we continued hearing the same Controller seem to struggle with communicating effectively; he seemed rather stressed or not entirely on his game. I recall the initial instruction; the initial clearance that was issued to us; as an instruction to Company and not the other carrier; and I did hear him after that incident occur a call or two that were stated incorrectly. I do believe the Captain also understood the same clearance and I do believe he might have questioned the clearance under normal circumstances but the radios were so busy there really wasn't much of a break and again; we both believed we heard the same thing.I'm not entirely sure what can be done. I wish I could hear the transmissions all over again. I think it's possible the other carrier aircraft ahead of us was on approach and we were unaware of his presence. Perhaps if ATC had notified us of a similar sounding call sign like they do quite often; that might have prevented some confusion; but that was not stated. I guess we could question the clearance; but for my part; I did not think the clearance was unreasonable; but since I lack experience in Atlanta that could have been part of the issue. But without a doubt the heavy frequency congestion added to the confusion and the inability to have a break to question ATC. I can't speak for the Captain; but maybe our clearance altitude indeed was so low that he should have verified it. But again; it was VMC; I could see other aircraft visually and on TCAS; I could see the terrain; I didn't think it was an unreasonable clearance to begin with. B737 flight crew reported becoming confused by similar sounding call signs during approach to ATL and mistakenly accepted a descent clearance meant for another aircraft.